mlsanityData to 7 Oct 2026

Split Gibbs Discrete Diffusion Posterior Sampling

arXiv 2503.01161 ↗First posted 3 Mar 2025cs.LG cs.CVcited by 18

On the map: Diffusion models → Inverse problems and image restoration

Abstract (arXiv)

We study the problem of posterior sampling in discrete-state spaces using discrete diffusion models. While posterior sampling methods for continuous diffusion models have achieved remarkable progress, analogous methods for discrete diffusion models remain challenging. In this work, we introduce a principled plug-and-play discrete diffusion posterior sampling algorithm based on split Gibbs sampling, which we call SGDD. Our algorithm enables reward-guided generation and solving inverse problems in discrete-state spaces. We demonstrate the convergence of SGDD to the target posterior distribution and verify this through controlled experiments on synthetic benchmarks. Our method enjoys state-of-the-art posterior sampling performance on a range of benchmarks for discrete data, including DNA sequence design, discrete image inverse problems, and music infilling, achieving more than 30% improved performance compared to existing baselines. Our code is available at https://github.com/chuwd19/Split-Gibbs-Discrete-Diffusion-Posterior-Sampling.

Key facts. Cited by 18 papers in the map (data through 7 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 40 of its 60 references that are in the map. First posted on arXiv 3 Mar 2025.

Builds on

40 of 60 references.

Closest ancestors · 12

Same direction, newest first

  1. 2024A Survey on Diffusion Models for Inverse Problems30 Sep
  2. 2024Ensemble Kalman Diffusion Guidance: A Derivative-free Method for Inverse Problems30 Sep
  3. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing1 Jul
  4. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors29 May
  5. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction25 Mar
  6. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency16 Jul
  7. 2023Denoising Diffusion Models for Plug-and-Play Image Restoration15 May
  8. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Models7 May
  9. 2023Score-Based Diffusion Models as Principled Priors for Inverse Imaging23 Apr
  10. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model1 Dec
  11. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  12. 2022Denoising Diffusion Restoration Models27 Jan

Other references · 28

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  3. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  4. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  5. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  6. 2020Taming Transformers for High-Resolution Image Synthesiscited by 3,229
  7. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  8. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
  9. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  10. 2023Discrete Diffusion Modeling by Estimating the Ratios of the Data Distributioncited by 712
  11. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
  12. 2022A Continuous Time Framework for Discrete Denoising Modelscited by 437
16 more
  1. 2023Analyzing and Improving the Training Dynamics of Diffusion Modelscited by 396
  2. 2021Score-based diffusion models for accelerated MRIcited by 308
  3. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
  4. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problemcited by 229
  5. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 218
  6. 2025A General Framework for Inference-time Scaling and Steering of Diffusion Modelscited by 201
  7. 2017MuseGAN: Multi-track Sequential Generative Adversarial Networks for Symbolic Music Generation and Accompanimentcited by 151
  8. 2024Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decodingcited by 127
  9. 2024Unlocking Guidance for Discrete State-Space Diffusion and Flow Modelscited by 124
  10. 2024Fine-Tuning Discrete Diffusion Models via Reward Optimization with Applications to DNA and Protein Designcited by 72
  11. 2022Towards a Theory of Non-Log-Concave Sampling: First-Order Stationarity Guarantees for Langevin Monte Carlocited by 63
  12. 2024Symbolic Music Generation with Non-Differentiable Rule Guided Diffusioncited by 52
  13. 2023Provable Probabilistic Imaging using Score-Based Generative Priorscited by 51
  14. 2018Split-and-augmented Gibbs sampler - Application to large-scale inference problemscited by 47
  15. 2023Plug-and-Play split Gibbs sampler: embedding deep generative priors in Bayesian inferencecited by 41
  16. 2025Debiasing Guidance for Discrete Diffusion with Sequential Monte Carlocited by 29

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 6; 2026: 12.

18 papers.

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  1. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  2. 2025Inference-Time Scaling of Discrete Diffusion Models via Importance Weighting and Optimal Proposal Designcited by 12
  3. 2025Steering Generative Models with Experimental Data for Protein Fitness Optimizationcited by 7
  4. 2025Test-Time Anchoring for Discrete Diffusion Posterior Samplingcited by 5
  5. 2025Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priorscited by 3
  6. 2026Reward-Guided Discrete Diffusion via Clean-Sample Markov Chain for Molecule and Biological Sequence Designcited by 3
  7. 2026Contrastive Distribution Matching for Amortized Sequential Monte Carlo in Discrete Diffusioncited by 3
  8. 2026Plug-and-Play Guidance for Discrete Diffusion Models via Gradient-Informed Logit Correctioncited by 3
  9. 2025Diffusion Alignment as Variational Expectation-Maximizationcited by 2
  10. 2026Entropy Aware Reward Guidance for Diffusion Language Model Alignmentcited by 2
  11. 2026SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogatecited by 2
  12. 2026From Scores to Gibbs Correctors: Accelerating Uniform-Rate Discrete Diffusion Modelscited by 1
6 more
  1. 2026FluxLite: Inference-Time Proposal Control for Discrete Diffusion Modelscited by 1
  2. 2026Plug-and-Play Diffusion Meets ADMM: Dual-Variable Coupling for Robust Medical Image Reconstructioncited by 0
  3. 2026Dependency-Aware Discrete Diffusion for Scene Graph Generationcited by 0
  4. 2026Discrete Langevin-Inspired Posterior Samplingcited by 0
  5. 2026VGAS: Variance-Reduced Guidance and Adaptive Selection for Training-Free Reward Alignment in Discrete Diffusioncited by 0
  6. 2026FlowSGS: Improving Flow Matching Priors for Inverse Imaging with Stochastic Interpolantscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors
  2. 2024Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors
  3. 2025Interleaved Gibbs Diffusion: Generating Discrete-Continuous Data with Implicit Constraints
  4. 2026Learning to Replace MCMC in Split-Gibbs Diffusion Posterior Sampling via Deep Unfolding
  5. 2025A Mixture-Based Framework for Guiding Diffusion Models
  6. 2025Exact Evaluation of the Accuracy of Diffusion Models for Inverse Problems with Gaussian Data Distributions
  7. 2024Posterior Sampling with Denoising Oracles via Tilted Transport
  8. 2026A Gibbs posterior sampler for inverse problem based on prior diffusion model